Find where the function is increasing.

[Ghost3k]

Could anyone help me confirm where the function is increasing.
Here is the function:

Here is my answer:

 

[tkhunny]

1) How do we know you didn't just copy this out of the back of the book?

2) Answer to question #1 - Show your work!

3) Why do you doubt?

 

[Someone2841]

Could anyone help me confirm where the function is increasing.
Here is the function:

Here is my answer:

It is possibly better to show your work along with your answer. That way, if you had gone wrong, someone could explain how/why. As it turns out, you have posted the correct solution to the problem. You probably did something like this:

As I'm sure you're aware, a function \(\displaystyle f(x)\) is increasing whenever \(\displaystyle f'(x)>0\). When \(\displaystyle f(x)=5x^{21}e^{-4x}\), then \(\displaystyle f'(x)=105x^{20}e^{-4x} - 20x^{21}e^{-4x}\). Therefore, this function is increasing whenever \(\displaystyle 105x^{20}e^{-4x} - 20x^{21}e^{-4x}>0\). We solve for \(\displaystyle x\) to understand that whenever \(\displaystyle x<21/4\) and \(\displaystyle x \neq 0\), the function is increasing. This is equivalent to the solution you provided.

 

[renegade05]

1) How do we know you didn't just copy this out of the back of the book?

Why would he ask for a confirmation if he copied it out of a text book?

 

[Ghost3k]

It is possibly better to show your work along with your answer. That way, if you had gone wrong, someone could explain how/why. As it turns out, you have posted the correct solution to the problem. You probably did something like this:

As I'm sure you're aware, a function \(\displaystyle f(x)\) is increasing whenever \(\displaystyle f'(x)>0\). When \(\displaystyle f(x)=5x^{21}e^{-4x}\), then \(\displaystyle f'(x)=105x^{20}e^{-4x} - 20x^{21}e^{-4x}\). Therefore, this function is increasing whenever \(\displaystyle 105x^{20}e^{-4x} - 20x^{21}e^{-4x}>0\). We solve for \(\displaystyle x\) to understand that whenever \(\displaystyle x<21/4\) and \(\displaystyle x \neq 0\), the function is increasing. This is equivalent to the solution you provided.

Thank You for the confirmation.

Why would he ask for a confirmation if he copied it out of a text book?

Thanks for the support renegade05, some people in this forum really are cynical. If you all must know, I'm doing online homework so no there are no answers from the back of the book, because there is no book. Also I had been working out that problem a few times but the website said it was wrong. However, I was sure that it was correct. So, I came here to the forum to confirm my answers to prove that the online hw had these problems incorrectly solved.

 

[renegade05]

Oh. I wasn't trying to start something, especially not with tk - he has helped me a lot in the past, and will prob need his help in the future.

I was just being funny more than anything...

 

[tkhunny]

No worries. We're all in this together and we'll stay in it together as long as simple suggestions are not taken as insults.

Serously, though -- show your work!